Problem: Simplify. Remove all perfect squares from inside the square roots. Assume $x$ and $y$ are positive. $\sqrt{8x^3y^2}=$
Explanation: $\begin{aligned} \sqrt{8x^3y^2}&=\sqrt{2^2\cdot x^2\cdot y^2\cdot 2x} \\\\ &=\sqrt{2^2}\cdot\sqrt{x^2}\cdot\sqrt{y^2}\cdot\sqrt{2x} \\\\ &=2\cdot x\cdot y\cdot\sqrt{2x} \\\\ &=2xy\sqrt{2x} \end{aligned}$ In conclusion, $\sqrt{8x^3y^2}=2xy\sqrt{2x}$